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Thursday, November 01, 2007

Groups, Lies, and Assholes

A while ago I was browsing the web for a book on Lie-Groups. I got several hits in the psychology department on lies, group psychology and self-deception, which was the inspiration for this post. Before I go on, a sentence for the pedagogic value of this blog: a Lie Group is maths thingy which underlies our current understanding of the Standard Model. It's named after Marius Sophus Lie, who was Norwegian, so the pronunciation is actually Lee-Group, and it's got nothing to do with lying.

Okay, that was about it with the scientific content of this post.

Now here comes my personal group theory, addressing the question what makes a group work well, such that members get along, act in common interest, are supportive to each other, are able to solve occurring problems within the group, as well as conflicts between the group and others. Most importantly, what is necessary for a group to succeed in working towards its goals?

Here is what Hollywood taught me: No matter what the size of the group, it needs at least sufficient members to fulfil four different tasks.

A SoulMost importantly the soul of a group reflects the group identity. He or she typically is the source of encouragement and motivation, the first to stand up after a defeat, the dreamer and the visionary. Though not necessarily a leader, he or she is the person who keeps the group alive by reassuring coherence. There's no working towards a goal without knowing the goal. In movies, the soul is typically the narrator or the hero of the story.

A BrainNothing works without somebody who knows how to make a vision reality. The brain's task is to work out the plan and take care of the details. He or she is usually an efficiently working no-fuzz person, and enables the group to practically get where vision aims at. In movies, the brain is often a scientist with a large nerd-factor, which provides a source for gags and jokes.

A HeartThe heart listens to concerns, offers comfort and is good with understanding the group member's individual problems. He or she is responsible for the human touch, usually very sensitive to internally occurring trouble, good with negotiation and has a skill for counseling. In movies the heart is often in conflict with #4...

An AssholeOr call it an outsider. The asshole's task is to criticize and to question the existence and goals of the group, to try differently, to stumble and fall. He or she typically offends group members with opinions that go against the group identity, but also prevents them from taking their self chosen task too seriously. In movies the asshole is usually responsible for the sarcasm and cynicism.

These functions need not necessarily be fulfilled by four different people. In some cases one person might fulfil several tasks, or one task might be shared among different people. 1 and 2 often need to cooperate when it comes to leadership and organizing group activities.

Can somebody fill me in whether it works for the A-team (can't recall the details) or the Desperate Housewives (I never saw it)? There are other examples that came into my mind, but few of you will know them (e.g. TKKG).

A common alteration of the theme is to internalize the asshole through self-doubts of the main character, which reduces the core group to three. This works better in books than in movies. Examples for this are Harry Potter (soul + asshole), Hermione (brain) and Ron (heart). Or there is the Lord of the Rings with Frodo (soul + asshole), Gandalf (brain) and Sam (heart).

Another frequently used modification is to export the brain to a mysterious outsider, or to the wisdom of a larger group, like e.g. Star Wars exports the brain to 'The Force', which leaves us with the soul -Luke, the heart - Leia, and the Asshole - Han Solo.

Of course you can have larger groups, but these four core functions are usually present among them, and most other characters are, except for their entertainment value, exchangeable.

What I found most interesting when I thought about it is the relevance of the outsider to the group's functionality. Most often, a plot wouldn't move anywhere without such a person.

:-) Very insightful. Though I think you use the term 'asshole' in a slightly different meaning than I do. If you want to push it, I'd say a group that contains only assholes is dysfunctional because it has no asshole.

Hi Anonymous:

How so? Didn't she always stay behind the mission? Sorry, it's been like ~10 years that I saw the movies last time, so please enlighten me.

Dear Arun:

Thanks for reminding me, I think I mentioned that movie elsewhere let me see ... here, but I had almost forgotten about it (if nothing else then the blog is good to show I had heard of 'it' before, whatever 'it' is). I can't say though it's the kind of movie that I'd call a must see. Do you plan on seeing it? If so, let me know whether it's worth the time.

Well, any suggestions for an actual Lie Groups book? As strange as it seems, I'm having trouble finding one for my needs: physical slant (but not too much crystallography), good coverage of the Lorentz group, ... Thanks anyway...

I think any successfull group needs an identity, or zero. It's usually easy to find a zero for a group - but you really can't afford to have more than one. If you add another member, then you will also need an inverse - someone who negates everything the second member does. Fortunately again, it's usually not hard to find someone who is his own inverse, so two element groups are also stable. With three element groups, it never works out unless you can get them to associate, and for four or more you can't even get them all to commute, so committee meetings are a real problem.

Lie Groups pose special problems since you can hardly ever get together enough people (infinitely many, for example) who can do the algebra - oh they all claim they can, but most Lie.

A Group can contain any types of people you want. However, a group tasked to perform work with defined result is more commonly called a Team. A team frequently contains the 4 types mentioned. But a team is doomed to failure without a type called Leader.

Well, yes, this was of course the actual reason for my search. The standard choice is Georgi's book which covers the basics. My problem is that a long time ago I had lecture notes from a Prof in our maths department which were much better, so I am still looking for a book that lives up to this.

Dear Arun:

There's no wrong and no right, and no spoon either ;-)

Hi Anonymous II:

No comment.

Hi CIP:

Yeah, truth spoken. That's why I don't do well in groups, there's usually no B^-1.

Hi Anonymous III:

Your comment about internalizing assholes was the last I read yesterday evening, I laughed my a** off ;-)

Hi Anonymous IV:

I am not a big believer in top-down approaches. Most often it's too cheap and fails easily. There might be somebody being an 'official' leader, but he needs people behind him. I don't think one person fulfilling all the 4 tasks above works very well. Esp. if you have a group with very intelligent people, leadership can be very difficult.

Hi Quasar:

Well, the torch is the guy who (in the movie) leaves the group and tries to get famous with his abilities. Samantha is the one who is rather cynical about love and relationships altogether (it's all about sex, obviously).

You probably don't remember me from my e-mail a couple of weeksago : I'm the guy with the Phd in algebra who makes a living asa petty beaureaucrat for the USDA and studies applications of algebra to physics on his own -- or at least tries to. So, first some books I've foundhelpful --

( 6 ) Emergence of the Theory of Lie Groups : An Essay in the History of Matematics- 1869-1926 ( Hawkins )

Well-told history with great periodphotos -- and a healthy dose of mathematics too - Some great anecdotes : Lie loved to hike aboutEurope ; to keep his clothes drywhen it rained, he would put his clothes in his backpack and hike in the nude !

I was please to find that, sinceI already knew something aboutgraded Lie algebras and Clifford-Lie algebras, I could read moreof this than I intially expected.

I am not much a part of any group lately - but not because I am the habitual 'asshole' --Would love to find study partnersfor applications of Clifford algebras in physics, and SUSY inparticular - I'd try to be the 'soul' of the group ---

thanks for the nice words, and the book suggestions - maybe I can have a look at some of them.

I learned about Lie groups and algebras in a seminar based on the Sattinger/Weaver text - that's really an interesting book, with many examples from very diverse backgrounds. But at times, it's easy to get lost because it touches so many topics.

But I am still looking for "the" book about Lie groups and algebras - those I've seen so far are either mathematical with some add-on physics, but where the connection (say, via a kind of dictionary math-physics) is quite loose, or physics books which are a bit sloppy on the side of maths...

Just wanted to thank bee and anonymous for the references... About Georgi's book, the irony is that my "requirement" about the good treatment of the Lorentz group was meant to exclude it ;) Anyway, in the same spirit (I think):

Soul: Hannibal, no question. Without his leadership, the team wouldn't have lasted a week. He kept them focused on their true role in the world -- helping those in need -- when otherwise they might have focused on making money and evading capture. It's because of Hannibal that the A-Team were heroes instead of merely being mercenaries.

Brain: Also Hannibal. "I love it when a plan comes together." It was almost always his plan. The others were tactically competent, but Hannibal was the one formulating strategy.

Heart: Murdock. Yes, he was crazy, but he was also upbeat and gung-ho, no matter how badly things went wrong. Murdock never gave up, never complained, always pulled his weight. You knew he had your back.

Asshole: B.A. and Face shared this role. Face did it mainly by whining about all the crap he had to put up with. B.A. did it by picking on Murdock and B.A. and doing his best to avoid getting on an airplane. But when all hell broke loose, both of them stopped bickering and charged into battle.